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Cryptocurrencies, Currency Competition, and the Impossible Trinity


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Cryptocurrencies, Currency Competition, and the Impossible Trinity

Pierpaolo Benigno*

Linda M. Schilling**

Harald Uhlig***


**Ecole Polytechnique CREST

***University of Chicago

July 2019



Global currencies are on the rise Facebook’s Libra 2020:

I backed by pool of low-risk assets and currencies

I Wide platform adoption already, 2.38 billion monthly active users as of 2019 (source: statista.com)

Bitcoin (2009):

I 32 million bitcoin wallets set up globally by December 2018 (source:




What makes global currency special?

National currency only

No medium of exchange abroad

Exchange to other national currency possible Exchange rate risk

With Global currency

Serves as medium of exchange in multiple countries

I No exchange rate risk

I But: Global currencies compete locally with national currency

I And: National currencies compete transnationally through global currency



What are the monetary policy Implications of introducing global currencies ?

Impossible Trinity: Under free capital flows, can have independent monetary policy when giving up a pegged exchange rate.

Main Result:

Free capital flows + global currency ⇒eliminates indep. Mon Policy Constraints Impossible Trinity



Currency Competition

Kareken and Wallace (1981), Manuelli and Peck (1990), Garratt and Wallace (2017), Schilling and Uhlig (2018)

Impossible Trinity

Fleming (1962), Mundell (1963)

Exchange Rate Dynamics and Currency Dominance

Obstfeld and Rogoff (1995); Casas, Diez, Gopinath, Gourinchas (2016)

Monetary Theory, Asset Pricing and Cryptocurrencies

Fern´andez-Villaverde and Sanches (2016), Benigno (2019), Biais, Bisiere, Bouvard, Casamatta, Menkveld (2018), Huberman, Leshno, Moallemi (2017)


Model I

discrete time, t= 0,1,2. . . 2 countries

1 tradeable consumption good

3 currencies: home H, foreign F, global G 2 sovereign bonds, Home and Foreign

1 representative, infinitely lived agent in each country

I utilityu(·) strictly increasing, continuous differentiable, concave

I discount factorβ(0,1)

I Intertemporal utility


Model II


Liquidity services:

I Lt in Home country,

I Lt in Foreign Exchange rates:

I Qt price of one unit global currency in terms of home currency,

I Qt price of one unit global currency in terms of foreign currency,

I St price of one unit foreign currency in terms of home currency Nominal Stochastic Discount Factors

I Home: Mt+1 I Foreign: Mt+1 Bonds

Nominal interest rates:

I it on bond in Home,

I it on bond in Foreign


Model III


Complete Markets:

Mt+1 =Mt+1 St St+1

(1) No arbitrage (uniqueness + existence SDF)

Liquidity Immediacy: The purchase of Home and Foreign currency yields an immediate liquidity service Lt, respctively Lt

No short sale on global currency (no neg. liquid service) No transaction costs




Q*t Qt





t t+1 t+2

1+it 1+i*t



Standard Asset pricing

Let R an arbitrary stochastic asset return, denominated in Home currency.

Intertemporal utility maximization of agents implies (Cochrane, 2008)

1 =Et[Mt+1Rt+1] (2)


Standard Asset pricing II

Equilibrium bond prices 1 1 +it

=Et[Mt+1] (3)


1 +it =Et[Mt+1 ] (4) Equilibrium currency prices


1 =Lt+Et[Mt+1] (5)

1 ≥




Qt ] (6)


1 =Lt +Et[Mt+1 ] (7) 1 ≥


Lt +Et[Mt+1 Qt+1

Qt ] (8)


Benchmark: No Global Currency

Equilibrium bond prices 1 1 +it

=Et[Mt+1] (9)


1 +it =Et[Mt+1 ] (10) Equilibrium currency prices


1 =Lt+Et[Mt+1] (11)

1 ≥




Qt ] (12)


1 =Lt +Et[Mt+1 ] (13)


Benchmark: No Global Currency II

Stochastic Uncovered Interest parity 0 =Et


(1 +it)St+1 St

−(1 +it)


⇒ Take-away: Absent direct currency competition L6=L, exchange rate Home-Foreign and interest rates are intertwined!


Results (1): With Global Currency


Global currency is valuedQt,Qt >0 Global currency used in both countries

Proposition 1 (Crypto-enforced Monetary Policy Synchronization) (i) The nominal interest rates on bonds have to be equal it =it

(ii) The liquidity services in Home and Foreign are equal Lt =Lt (iii) The nominal exchange rate between home and foreign currency follows a martingale under the risk-adjusted measure

t[St+1] :=Et[Mt+1St+1]

Et[Mt+1] =St (16)


Results: Economic Mechanism

A Introduction of Global currency creates global competition between national currencies

Local currency competition: Home⇔ Global Local currency competition: Foreign⇔ Global

Global currency competition: Home ⇔ Foreign (through Global) B direct competition between bonds

Local competition: Home currency⇔ home bond Local competition: Foreign currency⇔ foreign bond Global competition: Home bond⇔ Foreign bond (i =i) (Not UIP since without adjustment for exchange rates)


Results (2): With Global Currency


Global currency is valuedQt,Qt >0

National currencies are used in both countries Proposition 2 (Crowding Out)

Independently of whether the global currency is used in country f or not:

Ifit <it then

(i) the global currency is not adopted in country h (ii) The liquidity services satisfy Lt <Lt

(iii) The nominal exchange rate between home and foreign currency follows a supermartingale under the risk-adjusted measure of country h

˜ [S ] :=Et[Mt+1St+1]

<S (17)


Results: Economic Mechanism

Premise: At least one currency is used in each country

Interest rates and liquidity services are in one-to one relationship i ↔L,i ↔L

Bonds compete with currency nationally

If one country offers a lower interest rate it<it, also the liquidity services of currency in that country have to be lowerLt <Lt Global currency: Features additional risky return (exchange rate)

In contrast to the national currency, the global currency not only offers sure liquidity services.

market completeness, free capital flows and no arbitrage:

Expectations and pricing of the exchange rate of the global currency coincide internationally

⇒ Global currency is adopted in country with higher liquidity services (since GC overpriced in country with higher liquidity services)


Result (3): Losing control of medium of exchange


Global currency is valuedQt,Qt >0

Assume the global currency is used in country f Proposition 3 (Crowding Out)

If the CB in country h setsit >it then the national currency h is abandoned and the global currency takes over.


Asset-backed Global Currency


Assume a consortium of companies issues the global currency, backed by bonds of countryh

Assume that the consortium promises to trade any fixed amount of the global currency at fixed priceQt

to make money, the consortium charges a feeφt Qt+1= (1 +it−φt)Qt

Proposition 4 (Crowding Out) Assume the global currency is valued.

(i) Ifφt <it, then currency h is crowded out and only the global currency is used in country h

(ii) Ifφt =it: Both currencies h and the global currency coexist (iii) If φt >it: then only currency h is used

Insight: GC may combine best of both worlds, liquidity + interest. If φt >it, the consortium consumes the interest entirely.


Example 1: Money in Utility I

Consumers in Home have preferences Et0




u(ct) +v

MH,t+QtMG,t Pt

(18) budget constraint

BH,t+StBF,t+MH,t+QtMG,t =Wt+Pt(Yt−ct) (19)

u(·),v(·) concave

Pt,Pt price of consumption good in units of home and foreign currency

MH,t,MG,t money holdings in home resp. global currency BH,t,BF,t home resp. foreign bond holdings


Example 1: Money in Utility II


BH : uC(ct) Pt

1 1 +it


βuC(ct+1) Pt+1

(21) BF : uC(ct)

Pt 1

1 +it =Et

βuC(ct+1) Pt+1



(22) MH : uC(ct)



βuC(ct+1) Pt+1

+ 1



MH,t+QtMG,t Pt

(23) MG : Qt

uC(ct) Pt =Et

βQt+1uC(ct+1) Pt+1







Example 1: Money in Utility III

Matching Terms

Mt+1=βuC(ct+1) uC(ct)


Pt+1 (25)

Mt+1 =βuC(ct+1 ) uC(ct)


Pt+1 (26)

Lt = v0M

H,t+QtMG,t Pt

uC(ct) (27)

Lt =


F,t+QtMG,t Pt

uC(ct) (28)

⇒ In Equ. L=L



The introduction of a global currency

enforces direct competition between national currencies through the global currency

If all currencies are in use:

I crypto-enforced monetary policy synchronization (CEMPS)

I exchange rates become risk-adjusted martingales If interest rates differ:

I crowding out of currencies

I race down to ZLB


Praline: Deterministic Benchmark

Inflation Rates: πt= PPt

t−1 −1, πt= PPt t−1 −1 Real interest rates: rt=it−πt (Fisher)

Proposition 2 (Deterministic CMU)

(i) The liquidity services in Home and Foreign are equal Lt =Lt (ii) The nominal interest rates on bonds are equal it =it

(iii) The nominal exchange rate between home and foreign currency is constant St =S

⇒ inflation ratesπtt are the same

⇒ real interest ratesrt =rt are the same



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